QI have an Oceanus and a Sham-Nacha, Heir to Entwining on my field, and I evolve the latter, putting its crest into my EX area. When resolving Oceanus's triggered automatic ability, can I choose any number of options instead?

AYes. The crest would already be in your EX area by the time you need to resolve Oceanus's ability.

QIf my leader gains defense during my opponent's turn, does this amulet's ability still trigger?

AYes, it triggers regardless of whose turn it is.